Homogenizing a critical binary structure of finite diffusivities

Article type: Research Article

Authors: Gruais, Isabelle^; | Poliševski, Dan

Affiliations: Université de Rennes 1, I.R.M.A.R., Campus de Beaulieu, 35042 Rennes Cedex, France. E-mail: [email protected] | I.M.A.R., P.O. Box 1-764, Bucharest, Romania. E-mail: [email protected].

Note: [] Corresponding author.

Abstract: We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambient connected phase surrounding a suspension of very small spheres distributed in an ε-periodic network. We consider the critical radius case with finite diffusivities in both phases. The asymptotic distribution of the concentration is determined, as ε→0, assuming that the suspension has mass of unity order and vanishing volume. It appears that the ambient macroscopic concentration is satisfying a Volterra integro-differential equation and it is defining straightly the macroscopic concentration associated to the suspension.

Keywords: diffusion, homogenization, fine-scale substructure, Volterra integro-differential equation

Journal: Asymptotic Analysis, vol. 55, no. 1-2, pp. 85-101, 2007